A Multi-Scale Mathematical Modeling Study Of The Circulatory System

Cardiovascular diseases (CVDs) are world-wide leading cause of death. The pathological research, early prevention, diagnosis and treatment of CVDs are great challenges. Mathematical models of the circulatory system provide an effective auxiliary means for the physiological research, diagnosis and treatment of CVDs. The multi-scale mathematical modeling of the circulatory system focuses on studying the nature of multiphysics and multi-dimensional modeling techniques in coupling multiple levels of circulatory systems, namely systematic, organic and tissular levels. The models are able to help study the pathophysiology of CVDs quantitatively in multiple scales, and improve the standard of the prevention, diagnosis and treatment of CVDs.This study aims to build a multi-scale mathematical model of the circulatory system based on the key technologies in multi-scale modeling. The main contributions of this study are summarized as follows:1. Key technologies in the multi-scale modeling of the circulatory system were developed, including (1) the autonomic nervous system (ANS) modeling technique which can simulate heart rate variability;(2) the numerical computing technique which can improve the simulation efficiency of one-dimensional (ID) microcirculatory model;(3) the coupling technique which can link the systemic and" microcirculatory systems.2. By the incorporation of the systemic circulatory model and the ANS model, an index which characterizes the parasympathetic activity was proposed. The index was verified by use of clinical data, and its physiological mechanism was interpreted by the model simulation.3. A ID microcirculation model was created based on the experimental data of rat mesentery and conducted to simulate the damping of blood flow pulsatility. The model was validated against the experiment of the model animal. With the help of the model, it is discovered that the vascular resistance and compliance are the major factors of the damping of blood flow pulsatility.4. The systemic and microcirculatory systems were coupled by structural parameters. The simulation of the coupled model explored that the structural alterations in the microcirculation affect the systemic blood pressure level. The simulation result also suggested that the peripheral blood pressure pulsatility under hypertension was reduced, and thus might result in the dysfuntion of microcirculation.The main innovations of the study are:1. A multi-scale modeling technique is proposed based on the coupling of vascular resistance and compliance. The technique solves the problem of incorporating the systemic and microcirculatory systems, and thus provides a beneficial approach in studying the fusion of hemodynamic and functional properties in the models.2. With the help of the incorporation of the systemic circulatory model and the ANS model, a modified deceleration capacity index of heart rate is produced, and its superiority is validated in mechanism. The model technique provides a novel method for promoting the clinical use of ANS index.3. The high-performance numerical methods for1D microcirculation model were developed to permit the simulation of the damping of blood flow pulsatility. The model fills the gap of methodology in the physiological study of the pulsatility damping mechanism, and provides a promising framework for the mechanotransduction research in the microcirculation.In conclusion, the multi-scale mathematical models of the circulatory system provide an effective technological platform for quantitative research. With the further improvement and utilization, the models are potential to benefit the fundamental cardiovascular research and improve the cardiovascular health of the public.